A generalized matrix differential-algebraic equation
详细信息 查看全文
- 作者：Sergei M. Chuiko
- 关键词：Matrix boundary ; value problem ; differential ; algebraic equations ; generalized Green operator ; Sylvester equation
- 刊名：Journal of Mathematical Sciences
- 出版年：2015
- 出版时间：October 2015
- 年：2015
- 卷：210
- 期：1
- 页码：9-21
- 全文大小：217 KB
- 参考文献：1.N. V. Azbelev, N. P. Maksimov, and L. F. Rakhmatullina, Introduction to the Theory of Functional-Differential Equations [in Russian], Nauka, Moscow, 1991.
2.R. E. Bellman, Introduction to Matrix Analysis, McGraw-Hill, New York, 1987.
3.A. A. Boichuk and S. A. Krivosheya, 鈥淐riterion of the solvability of matrix equations of the Lyapunov type,鈥?Ukr. Math. J., 50, No. 8, 1162鈥?169 (1998).MathSciNet CrossRef
4.A. A. Boichuk and S. A. Krivosheya, 鈥淎 critical periodic boundary value problem for a matrix Riccati equations,鈥?Differ. Equa., 37, No. 4, 464鈥?71 (2001).MathSciNet CrossRef MATH
5.A. A. Boichuk, A. A. Pokutnyi, and V. F. Chistyakov, 鈥淎pplication of perturbation theory to the solvability analysis of differential algebraic equations,鈥?Comp. Math. Math. Phys., 53, No. 6, 777鈥?88 (2013).MathSciNet CrossRef
6.A. A. Boichuk and A. M. Samoilenko, Generalized Inverse Operators and Fredholm Boundary-Value Problems, VSP, Utrecht, Boston, 2004.CrossRef MATH
7.Yu. E. Boyarintsev and V. F. Chistyakov, Algebraic Differential Systems. Methods of Solution and Studies [in Russian], Nauka, Novosibirsk, 1998.
8.S. L. Campbell, Singular Systems of Differential Equations, Pitman, San Francisco, 1980.MATH
9.V. F. Chistyakov and A. A. Shcheglova, Selected Items of the Theory of Algebraic-Differential Systems [in Russian], Nauka, Novosibirsk, 2003.
10.S. M. Chuiko, 鈥淟inear Noetherian boundary-value problems for differential-algebraic systems,鈥?Computer Research and Modeling, 5, No. 5, 769鈥?83 (2013).MathSciNet
11.S. M. Chuiko, 鈥淟inear Noetherian boundary-value problem for a degenerate differential-algebraic system,鈥?Spect. Evol. Probl., 23, 148鈥?57 (2013).
12.S. M. Chuiko, 鈥淭he Green operator of a linear Noetherian boundary-value problem for a matrix differential equation,鈥?Dinam. Sist., 4 (32), Nos. 1鈥?, 101鈥?07 (2014).
13.S. M. Chuiko, 鈥淥n the solution of the Sylvester matrix equation,鈥?Vest. Odess. Nats. Univ. Ser. Mat. Mekh., 19, Issue 1 (21), 49鈥?7 (2014).
14.S. M. Chuiko, 鈥淥n the solution of the Lyapunov matrix equations,鈥?Vest. Khark. Nats. Univ. Im. V.N. Karazina. Ser. Mat., Prikl. Mat., Mekh., No. 1120, 85鈥?4 (2014).
15.S. M. Chuiko, 鈥淣oetherian boundary-value problems for degenerate differential-algebraic systems with linear pulse action,鈥?Dinam. Sist., 4 (32), Nos. 1鈥?, 89鈥?00 (2014).
16.S. M. Chuiko, 鈥淥n the solution of the generalized matrix Sylvester equation,鈥?Chebysh. Sb., 16, Issue 1, 52鈥?6 (2015).MathSciNet
17.V. P. Derevenskii, 鈥淏ernoulli matrix equations,鈥?Izv. Vuzov. Mat., No. 2, 14鈥?3 (2008).
18.A. M. Samoilenko, M. I. Shkil鈥? and V. P. Yakovets鈥? Linear Systems of Differential Equations with Degeneration [in Ukrainian], Vyshcha Shkola, Kyiv, 2000.
19.V. V. Voevodin and Yu. A. Kuznetsov, Matrices and Calculations [in Russian], Nauka, Moscow, 1984. - 作者单位：Sergei M. Chuiko (1)
1. Donbas State Pedagogical University, Slavyansk, Ukraine - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics
Russian Library of Science - 出版者：Springer New York
- ISSN：1573-8795
文摘
The conditions of solvability and the structure of the generalized Green operator of a linear Noetherian matrix differential-algebraic boundary-value problem are found. The sufficient conditions for reducibility of the generalized matrix differential-algebraic equation to the traditional differential-algebraic equation with the unknown function in the form of a vector-column are obtained. In the solution of a generalized matrix differential-algebraic boundary-value problem, the original conditions of solvability and the structure of the general solution of a matrix Sylvester-type equation are used. Keywords Matrix boundary-value problem differential-algebraic equations generalized Green operator Sylvester equation